CSSS 2008 Argentina-Readings
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CSSS Argentina 2008 |
Week 1 (tentative)
Forming project group teams
An important part of the school has to do with interacting with Faculty and your class mates. To foster this interaction interdisciplinary working groups will be formed. Each group will work on a project that will be presented by the end of the school. Projects are expected to elaborate on questions emerging from the working group internal brainstorming. Use the help and advise of the faculty around. They are open to interact and provide advise for the development of working group projects. And remember, the best way of tackling complexity is to aim for simplicity!
- Elizabeth Bradley (Nonlinear dynamics)
Definition of chaos; examples in various fields
An extended example: the logistic map. Introduce: bifurcations; bifurcation diagram and its structure, incl. Feigenbaum number; fractals and their connection to chaos
Continuous-time dynamics: definition
Introduce concepts: state variables, state space, trajectory, initial condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter
An extended example: the Lorenz system: history, physical meaning, trajectories, attractors, bifurcations (examples & definitions), types of attractors, stability: definition & mathematics, eigen. , un/stable manifolds, Lyapunov exponent and the connection to chaos
Numerical solvers: roles and issues
Shadowing
Projection vs section
Poincare sections in space & time
Delay-coordinate embedding
Examples: roulette, the SFI competition
Applications: filtering, control of chaos, synchronization & communication, spacecraft orbits, chaos in the solar system, harnessing the butterfly effect in fluids
Supporting Material:
Time Series Analysis - E. Bradley
Error in Numerical Methods - E. Bradley
Numerical Solution for Differential Equations - E. Bradley
Week 2
References:
-G. Nicolis and C. Nicolis, Foundations of Complex Systems, World Scientific, Singapore (2007).
-W. Ebeling and G. Nicolis, Word frequency and entropy of symbolic sequences: a dynamical perspective, Chaos Solitons and Fractals 2, 635 (1992).
-G. Nicolis and P. Gaspard, Toward a probabilistic approach to complex systems, Chaos Solitons and Fractals 4, 41 (1994).
-G. Nicolis, Thermodynamics today, Physica A213, 1 (1995).
-G. Nicolis and D. Daems, Probabilistic and thermodynamic aspects of dynamical systems, Chaos 8, 311 (1998).
-G. Nicolis, Nonequilibrium Statistical Mechanics, in Encyclopedia of Nonlinear Science, A. Scott ed., Routledge, New York (2005).
-P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge University Press, Cambridge (1998).
-P. Gaspard, Time-reversed dynamical entropy and irreversibility in Markovian random processes, J. Stat. Phys. 117, 599 (2004).
Supporting Material:
Complex Systems - Scholarpedia
Interdisciplinary Center for Nonlinear Phenomena and Complex Systems - G. Nicolis
Foundations of Complex Systems - G. Nicolis, C. Nicolis
Figure 1
Figure 2
Figure 3
Supporting Material:
Simple rules yield complex food webs - R. Williams & N. Martinez
Network Structure and biodiversity loss in food webs: robustness increases with connectance - J. Dunne, R. Williams & N. Martinez
Supporting Material:
Classical thermodynamics and economic general equilibrium theory - E. Smith & D. Foley
Thermodynamics of natural selection I: Energy flow and the limits of organization - E. Smith
Thermodynamics of natural selection II: Chemical Carnot cycles - E. Smith
Thermodynamics of natural selection III: Landauer's principle in computation and chemistry - E. Smith